Shane,
The Chromecast extension will only cast what appears in a tab in
Chrome (or full screen if enlarged from Chrome) to your TV set. JAWS 11 is, at
this point, in "the wayback machine" as far as web browser features go and I'm
not surprised that it is not announcing the pop-up/drop-down menu for
Chromecast. I just now tested with NVDA and it is announcing "Google Cast
Extension" when it lands on the button in Chrome's main control bar and is
announcing all the items, the first of which is "cast to {the name I gave my
Chromecast dongle}, followed by "separator," menu items options, send feedback,
and help.
I just looked at the Kodi.tv website and Kodi appears to be a
stand-alone media player program. I see no browser-related extensions/add-ins
on their site and searches on cast, casting, and Chromecast turn up nothing
that indicates Kodi and Chromecast can be used together in any way.
Brian